#include <math.h>

#include <stdlib.h>

#include <string.h>

#include <stdio.h>

#include <complex.h>

#ifdef complex

#undef complex

#endif

#ifdef I

#undef I

#endif

#if defined(_WIN64)

typedef long long BLASLONG;

typedef unsigned long long BLASULONG;

#else

typedef long BLASLONG;

typedef unsigned long BLASULONG;

#endif

#ifdef LAPACK_ILP64

typedef BLASLONG blasint;

#if defined(_WIN64)

#define blasabs(x) llabs(x)

#else

#define blasabs(x) labs(x)

#endif

#else

typedef int blasint;

#define blasabs(x) abs(x)

#endif

typedef blasint integer;

typedef unsigned int uinteger;

typedef char *address;

typedef short int shortint;

typedef float real;

typedef double doublereal;

typedef struct { real r, i; } complex;

typedef struct { doublereal r, i; } doublecomplex;

#ifdef _MSC_VER

static inline _Fcomplex Cf(complex *z) {_Fcomplex zz={z->r , z->i}; return zz;}

static inline _Dcomplex Cd(doublecomplex *z) {_Dcomplex zz={z->r , z->i};return zz;}

static inline _Fcomplex * _pCf(complex *z) {return (_Fcomplex*)z;}

static inline _Dcomplex * _pCd(doublecomplex *z) {return (_Dcomplex*)z;}

#else

static inline _Complex float Cf(complex *z) {return z->r + z->i*_Complex_I;}

static inline _Complex double Cd(doublecomplex *z) {return z->r + z->i*_Complex_I;}

static inline _Complex float * _pCf(complex *z) {return (_Complex float*)z;}

static inline _Complex double * _pCd(doublecomplex *z) {return (_Complex double*)z;}

#endif

#define pCf(z) (*_pCf(z))

#define pCd(z) (*_pCd(z))

typedef blasint logical;

typedef char logical1;

typedef char integer1;

#define TRUE_ (1)

#define FALSE_ (0)

/* Extern is for use with -E */

#ifndef Extern

#define Extern extern

#endif

/* I/O stuff */

typedef int flag;

typedef int ftnlen;

typedef int ftnint;

/*external read, write*/

typedef struct

{ flag cierr;

ftnint ciunit;

flag ciend;

char *cifmt;

ftnint cirec;

} cilist;

/*internal read, write*/

typedef struct

{ flag icierr;

char *iciunit;

flag iciend;

char *icifmt;

ftnint icirlen;

ftnint icirnum;

} icilist;

/*open*/

typedef struct

{ flag oerr;

ftnint ounit;

char *ofnm;

ftnlen ofnmlen;

char *osta;

char *oacc;

char *ofm;

ftnint orl;

char *oblnk;

} olist;

/*close*/

typedef struct

{ flag cerr;

ftnint cunit;

char *csta;

} cllist;

/*rewind, backspace, endfile*/

typedef struct

{ flag aerr;

ftnint aunit;

} alist;

/* inquire */

typedef struct

{ flag inerr;

ftnint inunit;

char *infile;

ftnlen infilen;

ftnint *inex; /*parameters in standard's order*/

ftnint *inopen;

ftnint *innum;

ftnint *innamed;

char *inname;

ftnlen innamlen;

char *inacc;

ftnlen inacclen;

char *inseq;

ftnlen inseqlen;

char *indir;

ftnlen indirlen;

char *infmt;

ftnlen infmtlen;

char *inform;

ftnint informlen;

char *inunf;

ftnlen inunflen;

ftnint *inrecl;

ftnint *innrec;

char *inblank;

ftnlen inblanklen;

} inlist;

#define VOID void

union Multitype { /* for multiple entry points */

integer1 g;

shortint h;

integer i;

/* longint j; */

real r;

doublereal d;

complex c;

doublecomplex z;

};

typedef union Multitype Multitype;

struct Vardesc { /* for Namelist */

};

typedef struct Vardesc Vardesc;

struct Namelist {

};

typedef struct Namelist Namelist;

#define abs(x) ((x) >= 0 ? (x) : -(x))

#define dabs(x) (fabs(x))

#define f2cmin(a,b) ((a) <= (b) ? (a) : (b))

#define f2cmax(a,b) ((a) >= (b) ? (a) : (b))

#define dmin(a,b) (f2cmin(a,b))

#define dmax(a,b) (f2cmax(a,b))

#define bit_test(a,b) ((a) >> (b) & 1)

#define bit_clear(a,b) ((a) & ~((uinteger)1 << (b)))

#define bit_set(a,b) ((a) | ((uinteger)1 << (b)))

#define abort_() { sig_die("Fortran abort routine called", 1); }

#define c_abs(z) (cabsf(Cf(z)))

#define c_cos(R,Z) { pCf(R)=ccos(Cf(Z)); }

#ifdef _MSC_VER

#define c_div(c, a, b) {Cf(c)._Val[0] = (Cf(a)._Val[0]/Cf(b)._Val[0]); Cf(c)._Val[1]=(Cf(a)._Val[1]/Cf(b)._Val[1]);}

#define z_div(c, a, b) {Cd(c)._Val[0] = (Cd(a)._Val[0]/Cd(b)._Val[0]); Cd(c)._Val[1]=(Cd(a)._Val[1]/df(b)._Val[1]);}

#else

#define c_div(c, a, b) {pCf(c) = Cf(a)/Cf(b);}

#define z_div(c, a, b) {pCd(c) = Cd(a)/Cd(b);}

#endif

#define c_exp(R, Z) {pCf(R) = cexpf(Cf(Z));}

#define c_log(R, Z) {pCf(R) = clogf(Cf(Z));}

#define c_sin(R, Z) {pCf(R) = csinf(Cf(Z));}

//#define c_sqrt(R, Z) {*(R) = csqrtf(Cf(Z));}

#define c_sqrt(R, Z) {pCf(R) = csqrtf(Cf(Z));}

#define d_abs(x) (fabs(*(x)))

#define d_acos(x) (acos(*(x)))

#define d_asin(x) (asin(*(x)))

#define d_atan(x) (atan(*(x)))

#define d_atn2(x, y) (atan2(*(x),*(y)))

#define d_cnjg(R, Z) { pCd(R) = conj(Cd(Z)); }

#define r_cnjg(R, Z) { pCf(R) = conjf(Cf(Z)); }

#define d_cos(x) (cos(*(x)))

#define d_cosh(x) (cosh(*(x)))

#define d_dim(__a, __b) ( *(__a) > *(__b) ? *(__a) - *(__b) : 0.0 )

#define d_exp(x) (exp(*(x)))

#define d_imag(z) (cimag(Cd(z)))

#define r_imag(z) (cimagf(Cf(z)))

#define d_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))

#define r_int(__x) (*(__x)>0 ? floor(*(__x)) : -floor(- *(__x)))

#define d_lg10(x) ( 0.43429448190325182765 * log(*(x)) )

#define r_lg10(x) ( 0.43429448190325182765 * log(*(x)) )

#define d_log(x) (log(*(x)))

#define d_mod(x, y) (fmod(*(x), *(y)))

#define u_nint(__x) ((__x)>=0 ? floor((__x) + .5) : -floor(.5 - (__x)))

#define d_nint(x) u_nint(*(x))

#define u_sign(__a,__b) ((__b) >= 0 ? ((__a) >= 0 ? (__a) : -(__a)) : -((__a) >= 0 ? (__a) : -(__a)))

#define d_sign(a,b) u_sign(*(a),*(b))

#define r_sign(a,b) u_sign(*(a),*(b))

#define d_sin(x) (sin(*(x)))

#define d_sinh(x) (sinh(*(x)))

#define d_sqrt(x) (sqrt(*(x)))

#define d_tan(x) (tan(*(x)))

#define d_tanh(x) (tanh(*(x)))

#define i_abs(x) abs(*(x))

#define i_dnnt(x) ((integer)u_nint(*(x)))

#define i_len(s, n) (n)

#define i_nint(x) ((integer)u_nint(*(x)))

#define i_sign(a,b) ((integer)u_sign((integer)*(a),(integer)*(b)))

#define pow_dd(ap, bp) ( pow(*(ap), *(bp)))

#define pow_si(B,E) spow_ui(*(B),*(E))

#define pow_ri(B,E) spow_ui(*(B),*(E))

#define pow_di(B,E) dpow_ui(*(B),*(E))

#define pow_zi(p, a, b) {pCd(p) = zpow_ui(Cd(a), *(b));}

#define pow_ci(p, a, b) {pCf(p) = cpow_ui(Cf(a), *(b));}

#define pow_zz(R,A,B) {pCd(R) = cpow(Cd(A),*(B));}

#define s_cat(lpp, rpp, rnp, np, llp) { ftnlen i, nc, ll; char *f__rp, *lp; ll = (llp); lp = (lpp); for(i=0; i < (int)*(np); ++i) { nc = ll; if((rnp)[i] < nc) nc = (rnp)[i]; ll -= nc; f__rp = (rpp)[i]; while(--nc >= 0) *lp++ = *(f__rp)++; } while(--ll >= 0) *lp++ = ' '; }

#define s_cmp(a,b,c,d) ((integer)strncmp((a),(b),f2cmin((c),(d))))

#define s_copy(A,B,C,D) { int __i,__m; for (__i=0, __m=f2cmin((C),(D)); __i<__m && (B)[__i] != 0; ++__i) (A)[__i] = (B)[__i]; }

#define sig_die(s, kill) { exit(1); }

#define s_stop(s, n) {exit(0);}

static char junk[] = "\n@(#)LIBF77 VERSION 19990503\n";

#define z_abs(z) (cabs(Cd(z)))

#define z_exp(R, Z) {pCd(R) = cexp(Cd(Z));}

#define z_sqrt(R, Z) {pCd(R) = csqrt(Cd(Z));}

#define myexit_() break;

#define mycycle() continue;

#define myceiling(w) {ceil(w)}

#define myhuge(w) {HUGE_VAL}

//#define mymaxloc_(w,s,e,n) {if (sizeof(*(w)) == sizeof(double)) dmaxloc_((w),*(s),*(e),n); else dmaxloc_((w),*(s),*(e),n);}

#define mymaxloc(w,s,e,n) {dmaxloc_(w,*(s),*(e),n)}

/* procedure parameter types for -A and -C++ */

#ifdef __cplusplus

typedef logical (*L_fp)(...);

#else

typedef logical (*L_fp)();

#endif

static float spow_ui(float x, integer n) {

float pow=1.0; unsigned long int u;

if(n != 0) {

if(n < 0) n = -n, x = 1/x;

for(u = n; ; ) {

if(u & 01) pow *= x;

if(u >>= 1) x *= x;

else break;

}

}

return pow;

}

static double dpow_ui(double x, integer n) {

double pow=1.0; unsigned long int u;

if(n != 0) {

if(n < 0) n = -n, x = 1/x;

for(u = n; ; ) {

if(u & 01) pow *= x;

if(u >>= 1) x *= x;

else break;

}

}

return pow;

}

#ifdef _MSC_VER

static _Fcomplex cpow_ui(complex x, integer n) {

complex pow={1.0,0.0}; unsigned long int u;

if(n != 0) {

if(n < 0) n = -n, x.r = 1/x.r, x.i=1/x.i;

for(u = n; ; ) {

if(u & 01) pow.r *= x.r, pow.i *= x.i;

if(u >>= 1) x.r *= x.r, x.i *= x.i;

else break;

}

}

_Fcomplex p={pow.r, pow.i};

return p;

}

#else

static _Complex float cpow_ui(_Complex float x, integer n) {

_Complex float pow=1.0; unsigned long int u;

if(n != 0) {

if(n < 0) n = -n, x = 1/x;

for(u = n; ; ) {

if(u & 01) pow *= x;

if(u >>= 1) x *= x;

else break;

}

}

return pow;

}

#endif

#ifdef _MSC_VER

static _Dcomplex zpow_ui(_Dcomplex x, integer n) {

_Dcomplex pow={1.0,0.0}; unsigned long int u;

if(n != 0) {

if(n < 0) n = -n, x._Val[0] = 1/x._Val[0], x._Val[1] =1/x._Val[1];

for(u = n; ; ) {

if(u & 01) pow._Val[0] *= x._Val[0], pow._Val[1] *= x._Val[1];

if(u >>= 1) x._Val[0] *= x._Val[0], x._Val[1] *= x._Val[1];

else break;

}

}

_Dcomplex p = {pow._Val[0], pow._Val[1]};

return p;

}

#else

static _Complex double zpow_ui(_Complex double x, integer n) {

_Complex double pow=1.0; unsigned long int u;

if(n != 0) {

if(n < 0) n = -n, x = 1/x;

for(u = n; ; ) {

if(u & 01) pow *= x;

if(u >>= 1) x *= x;

else break;

}

}

return pow;

}

#endif

static integer pow_ii(integer x, integer n) {

integer pow; unsigned long int u;

if (n <= 0) {

if (n == 0 || x == 1) pow = 1;

else if (x != -1) pow = x == 0 ? 1/x : 0;

else n = -n;

}

if ((n > 0) || !(n == 0 || x == 1 || x != -1)) {

u = n;

for(pow = 1; ; ) {

if(u & 01) pow *= x;

if(u >>= 1) x *= x;

else break;

}

}

return pow;

}

static integer dmaxloc_(double *w, integer s, integer e, integer *n)

{

double m; integer i, mi;

for(m=w[s-1], mi=s, i=s+1; i<=e; i++)

if (w[i-1]>m) mi=i ,m=w[i-1];

return mi-s+1;

}

static integer smaxloc_(float *w, integer s, integer e, integer *n)

{

float m; integer i, mi;

for(m=w[s-1], mi=s, i=s+1; i<=e; i++)

if (w[i-1]>m) mi=i ,m=w[i-1];

return mi-s+1;

}

static inline void cdotc_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {

integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

_Fcomplex zdotc = {0.0, 0.0};

if (incx == 1 && incy == 1) {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc._Val[0] += conjf(Cf(&x[i]))._Val[0] * Cf(&y[i])._Val[0];

zdotc._Val[1] += conjf(Cf(&x[i]))._Val[1] * Cf(&y[i])._Val[1];

}

} else {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc._Val[0] += conjf(Cf(&x[i*incx]))._Val[0] * Cf(&y[i*incy])._Val[0];

zdotc._Val[1] += conjf(Cf(&x[i*incx]))._Val[1] * Cf(&y[i*incy])._Val[1];

}

}

pCf(z) = zdotc;

}

#else

_Complex float zdotc = 0.0;

if (incx == 1 && incy == 1) {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc += conjf(Cf(&x[i])) * Cf(&y[i]);

}

} else {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc += conjf(Cf(&x[i*incx])) * Cf(&y[i*incy]);

}

}

pCf(z) = zdotc;

}

#endif

static inline void zdotc_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {

integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

_Dcomplex zdotc = {0.0, 0.0};

if (incx == 1 && incy == 1) {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc._Val[0] += conj(Cd(&x[i]))._Val[0] * Cd(&y[i])._Val[0];

zdotc._Val[1] += conj(Cd(&x[i]))._Val[1] * Cd(&y[i])._Val[1];

}

} else {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc._Val[0] += conj(Cd(&x[i*incx]))._Val[0] * Cd(&y[i*incy])._Val[0];

zdotc._Val[1] += conj(Cd(&x[i*incx]))._Val[1] * Cd(&y[i*incy])._Val[1];

}

}

pCd(z) = zdotc;

}

#else

_Complex double zdotc = 0.0;

if (incx == 1 && incy == 1) {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc += conj(Cd(&x[i])) * Cd(&y[i]);

}

} else {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc += conj(Cd(&x[i*incx])) * Cd(&y[i*incy]);

}

}

pCd(z) = zdotc;

}

#endif

static inline void cdotu_(complex *z, integer *n_, complex *x, integer *incx_, complex *y, integer *incy_) {

integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

_Fcomplex zdotc = {0.0, 0.0};

if (incx == 1 && incy == 1) {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc._Val[0] += Cf(&x[i])._Val[0] * Cf(&y[i])._Val[0];

zdotc._Val[1] += Cf(&x[i])._Val[1] * Cf(&y[i])._Val[1];

}

} else {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc._Val[0] += Cf(&x[i*incx])._Val[0] * Cf(&y[i*incy])._Val[0];

zdotc._Val[1] += Cf(&x[i*incx])._Val[1] * Cf(&y[i*incy])._Val[1];

}

}

pCf(z) = zdotc;

}

#else

_Complex float zdotc = 0.0;

if (incx == 1 && incy == 1) {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc += Cf(&x[i]) * Cf(&y[i]);

}

} else {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc += Cf(&x[i*incx]) * Cf(&y[i*incy]);

}

}

pCf(z) = zdotc;

}

#endif

static inline void zdotu_(doublecomplex *z, integer *n_, doublecomplex *x, integer *incx_, doublecomplex *y, integer *incy_) {

integer n = *n_, incx = *incx_, incy = *incy_, i;

#ifdef _MSC_VER

_Dcomplex zdotc = {0.0, 0.0};

if (incx == 1 && incy == 1) {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc._Val[0] += Cd(&x[i])._Val[0] * Cd(&y[i])._Val[0];

zdotc._Val[1] += Cd(&x[i])._Val[1] * Cd(&y[i])._Val[1];

}

} else {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc._Val[0] += Cd(&x[i*incx])._Val[0] * Cd(&y[i*incy])._Val[0];

zdotc._Val[1] += Cd(&x[i*incx])._Val[1] * Cd(&y[i*incy])._Val[1];

}

}

pCd(z) = zdotc;

}

#else

_Complex double zdotc = 0.0;

if (incx == 1 && incy == 1) {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc += Cd(&x[i]) * Cd(&y[i]);

}

} else {

for (i=0;i<n;i++) { /* zdotc = zdotc + dconjg(x(i))* y(i) */

zdotc += Cd(&x[i*incx]) * Cd(&y[i*incy]);

}

}

pCd(z) = zdotc;

}

#endif

/* -- translated by f2c (version 20000121).

You must link the resulting object file with the libraries:

-lf2c -lm (in that order)

*/

/* -- translated by f2c (version 20000121).

You must link the resulting object file with the libraries:

-lf2c -lm (in that order)

*/

/* -- translated by f2c (version 20000121).

You must link the resulting object file with the libraries:

-lf2c -lm (in that order)

*/

/* Table of constant values */

static integer c__1 = 1;

/* > \brief <b> CGBSVX computes the solution to system of linear equations A * X = B for GB matrices</b> */

/* =========== DOCUMENTATION =========== */

/* Online html documentation available at */

/* http://www.netlib.org/lapack/explore-html/ */

/* > \htmlonly */

/* > Download CGBSVX + dependencies */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/cgbsvx.

f"> */

/* > [TGZ]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/cgbsvx.

f"> */

/* > [ZIP]</a> */

/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/cgbsvx.

f"> */

/* > [TXT]</a> */

/* > \endhtmlonly */

/* Definition: */

/* =========== */

/* SUBROUTINE CGBSVX( FACT, TRANS, N, KL, KU, NRHS, AB, LDAB, AFB, */

/* LDAFB, IPIV, EQUED, R, C, B, LDB, X, LDX, */

/* RCOND, FERR, BERR, WORK, RWORK, INFO ) */

/* CHARACTER EQUED, FACT, TRANS */

/* INTEGER INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N, NRHS */

/* REAL RCOND */

/* INTEGER IPIV( * ) */

/* REAL BERR( * ), C( * ), FERR( * ), R( * ), */

/* $ RWORK( * ) */

/* COMPLEX AB( LDAB, * ), AFB( LDAFB, * ), B( LDB, * ), */

/* $ WORK( * ), X( LDX, * ) */

/* > \par Purpose: */

/* ============= */

/* > */

/* > \verbatim */

/* > */

/* > CGBSVX uses the LU factorization to compute the solution to a complex */

/* > system of linear equations A * X = B, A**T * X = B, or A**H * X = B, */

/* > where A is a band matrix of order N with KL subdiagonals and KU */

/* > superdiagonals, and X and B are N-by-NRHS matrices. */

/* > */

/* > Error bounds on the solution and a condition estimate are also */

/* > provided. */

/* > \endverbatim */

/* > \par Description: */

/* ================= */

/* > */

/* > \verbatim */

/* > */

/* > The following steps are performed by this subroutine: */

/* > */

/* > 1. If FACT = 'E', real scaling factors are computed to equilibrate */

/* > the system: */

/* > TRANS = 'N': diag(R)*A*diag(C) *inv(diag(C))*X = diag(R)*B */

/* > TRANS = 'T': (diag(R)*A*diag(C))**T *inv(diag(R))*X = diag(C)*B */

/* > TRANS = 'C': (diag(R)*A*diag(C))**H *inv(diag(R))*X = diag(C)*B */

/* > Whether or not the system will be equilibrated depends on the */

/* > scaling of the matrix A, but if equilibration is used, A is */

/* > overwritten by diag(R)*A*diag(C) and B by diag(R)*B (if TRANS='N') */

/* > or diag(C)*B (if TRANS = 'T' or 'C'). */

/* > */

/* > 2. If FACT = 'N' or 'E', the LU decomposition is used to factor the */

/* > matrix A (after equilibration if FACT = 'E') as */

/* > A = L * U, */

/* > where L is a product of permutation and unit lower triangular */

/* > matrices with KL subdiagonals, and U is upper triangular with */

/* > KL+KU superdiagonals. */

/* > */

/* > 3. If some U(i,i)=0, so that U is exactly singular, then the routine */

/* > returns with INFO = i. Otherwise, the factored form of A is used */

/* > to estimate the condition number of the matrix A. If the */

/* > reciprocal of the condition number is less than machine precision, */

/* > INFO = N+1 is returned as a warning, but the routine still goes on */

/* > to solve for X and compute error bounds as described below. */

/* > */

/* > 4. The system of equations is solved for X using the factored form */

/* > of A. */

/* > */

/* > 5. Iterative refinement is applied to improve the computed solution */

/* > matrix and calculate error bounds and backward error estimates */

/* > for it. */

/* > */

/* > 6. If equilibration was used, the matrix X is premultiplied by */

/* > diag(C) (if TRANS = 'N') or diag(R) (if TRANS = 'T' or 'C') so */

/* > that it solves the original system before equilibration. */

/* > \endverbatim */

/* Arguments: */

/* ========== */

/* > \param[in] FACT */

/* > \verbatim */

/* > FACT is CHARACTER*1 */

/* > Specifies whether or not the factored form of the matrix A is */

/* > supplied on entry, and if not, whether the matrix A should be */

/* > equilibrated before it is factored. */

/* > = 'F': On entry, AFB and IPIV contain the factored form of */

/* > A. If EQUED is not 'N', the matrix A has been */

/* > equilibrated with scaling factors given by R and C. */

/* > AB, AFB, and IPIV are not modified. */

/* > = 'N': The matrix A will be copied to AFB and factored. */

/* > = 'E': The matrix A will be equilibrated if necessary, then */

/* > copied to AFB and factored. */

/* > \endverbatim */

/* > */

/* > \param[in] TRANS */

/* > \verbatim */

/* > TRANS is CHARACTER*1 */

/* > Specifies the form of the system of equations. */

/* > = 'N': A * X = B (No transpose) */

/* > = 'T': A**T * X = B (Transpose) */

/* > = 'C': A**H * X = B (Conjugate transpose) */

/* > \endverbatim */

/* > */

/* > \param[in] N */

/* > \verbatim */

/* > N is INTEGER */

/* > The number of linear equations, i.e., the order of the */

/* > matrix A. N >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] KL */

/* > \verbatim */

/* > KL is INTEGER */

/* > The number of subdiagonals within the band of A. KL >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] KU */

/* > \verbatim */

/* > KU is INTEGER */

/* > The number of superdiagonals within the band of A. KU >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in] NRHS */

/* > \verbatim */

/* > NRHS is INTEGER */

/* > The number of right hand sides, i.e., the number of columns */

/* > of the matrices B and X. NRHS >= 0. */

/* > \endverbatim */

/* > */

/* > \param[in,out] AB */

/* > \verbatim */

/* > AB is COMPLEX array, dimension (LDAB,N) */

/* > On entry, the matrix A in band storage, in rows 1 to KL+KU+1. */

/* > The j-th column of A is stored in the j-th column of the */

/* > array AB as follows: */

/* > AB(KU+1+i-j,j) = A(i,j) for f2cmax(1,j-KU)<=i<=f2cmin(N,j+kl) */

/* > */

/* > If FACT = 'F' and EQUED is not 'N', then A must have been */

/* > equilibrated by the scaling factors in R and/or C. AB is not */

/* > modified if FACT = 'F' or 'N', or if FACT = 'E' and */

/* > EQUED = 'N' on exit. */

/* > */

/* > On exit, if EQUED .ne. 'N', A is scaled as follows: */

/* > EQUED = 'R': A := diag(R) * A */

/* > EQUED = 'C': A := A * diag(C) */

/* > EQUED = 'B': A := diag(R) * A * diag(C). */

/* > \endverbatim */

/* > */

/* > \param[in] LDAB */

/* > \verbatim */

/* > LDAB is INTEGER */

/* > The leading dimension of the array AB. LDAB >= KL+KU+1. */

/* > \endverbatim */

/* > */

/* > \param[in,out] AFB */

/* > \verbatim */

/* > AFB is COMPLEX array, dimension (LDAFB,N) */

/* > If FACT = 'F', then AFB is an input argument and on entry */

/* > contains details of the LU factorization of the band matrix */

/* > A, as computed by CGBTRF. U is stored as an upper triangular */

/* > band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, */

/* > and the multipliers used during the factorization are stored */

/* > in rows KL+KU+2 to 2*KL+KU+1. If EQUED .ne. 'N', then AFB is */

/* > the factored form of the equilibrated matrix A. */

/* > */

/* > If FACT = 'N', then AFB is an output argument and on exit */

/* > returns details of the LU factorization of A. */

/* > */

/* > If FACT = 'E', then AFB is an output argument and on exit */

/* > returns details of the LU factorization of the equilibrated */

/* > matrix A (see the description of AB for the form of the */

/* > equilibrated matrix). */

/* > \endverbatim */

/* > */

/* > \param[in] LDAFB */

/* > \verbatim */

/* > LDAFB is INTEGER */

/* > The leading dimension of the array AFB. LDAFB >= 2*KL+KU+1. */

/* > \endverbatim */

/* > */

/* > \param[in,out] IPIV */

/* > \verbatim */

/* > IPIV is INTEGER array, dimension (N) */

/* > If FACT = 'F', then IPIV is an input argument and on entry */

/* > contains the pivot indices from the factorization A = L*U */

/* > as computed by CGBTRF; row i of the matrix was interchanged */

/* > with row IPIV(i). */

/* > */

/* > If FACT = 'N', then IPIV is an output argument and on exit */

/* > contains the pivot indices from the factorization A = L*U */

/* > of the original matrix A. */

/* > */

/* > If FACT = 'E', then IPIV is an output argument and on exit */

/* > contains the pivot indices from the factorization A = L*U */

/* > of the equilibrated matrix A. */

/* > \endverbatim */

/* > */

/* > \param[in,out] EQUED */

/* > \verbatim */

/* > EQUED is CHARACTER*1 */

/* > Specifies the form of equilibration that was done. */

/* > = 'N': No equilibration (always true if FACT = 'N'). */

/* > = 'R': Row equilibration, i.e., A has been premultiplied by */

/* > diag(R). */

/* > = 'C': Column equilibration, i.e., A has been postmultiplied */

/* > by diag(C). */

/* > = 'B': Both row and column equilibration, i.e., A has been */

/* > replaced by diag(R) * A * diag(C). */

/* > EQUED is an input argument if FACT = 'F'; otherwise, it is an */

/* > output argument. */

/* > \endverbatim */

/* > */

/* > \param[in,out] R */

/* > \verbatim */

/* > R is REAL array, dimension (N) */

/* > The row scale factors for A. If EQUED = 'R' or 'B', A is */

/* > multiplied on the left by diag(R); if EQUED = 'N' or 'C', R */

/* > is not accessed. R is an input argument if FACT = 'F'; */

/* > otherwise, R is an output argument. If FACT = 'F' and */

/* > EQUED = 'R' or 'B', each element of R must be positive. */

/* > \endverbatim */

/* > */

/* > \param[in,out] C */

/* > \verbatim */

/* > C is REAL array, dimension (N) */

/* > The column scale factors for A. If EQUED = 'C' or 'B', A is */

/* > multiplied on the right by diag(C); if EQUED = 'N' or 'R', C */

/* > is not accessed. C is an input argument if FACT = 'F'; */

/* > otherwise, C is an output argument. If FACT = 'F' and */

/* > EQUED = 'C' or 'B', each element of C must be positive. */

/* > \endverbatim */

/* > */

/* > \param[in,out] B */

/* > \verbatim */

/* > B is COMPLEX array, dimension (LDB,NRHS) */

/* > On entry, the right hand side matrix B. */

/* > On exit, */

/* > if EQUED = 'N', B is not modified; */

/* > if TRANS = 'N' and EQUED = 'R' or 'B', B is overwritten by */

/* > diag(R)*B; */

/* > if TRANS = 'T' or 'C' and EQUED = 'C' or 'B', B is */

/* > overwritten by diag(C)*B. */

/* > \endverbatim */

/* > */

/* > \param[in] LDB */

/* > \verbatim */

/* > LDB is INTEGER */

/* > The leading dimension of the array B. LDB >= f2cmax(1,N). */

/* > \endverbatim */

/* > */

/* > \param[out] X */

/* > \verbatim */

/* > X is COMPLEX array, dimension (LDX,NRHS) */

/* > If INFO = 0 or INFO = N+1, the N-by-NRHS solution matrix X */

/* > to the original system of equations. Note that A and B are */

/* > modified on exit if EQUED .ne. 'N', and the solution to the */

/* > equilibrated system is inv(diag(C))*X if TRANS = 'N' and */

/* > EQUED = 'C' or 'B', or inv(diag(R))*X if TRANS = 'T' or 'C' */

/* > and EQUED = 'R' or 'B'. */

/* > \endverbatim */

/* > */

/* > \param[in] LDX */

/* > \verbatim */

/* > LDX is INTEGER */

/* > The leading dimension of the array X. LDX >= f2cmax(1,N). */

/* > \endverbatim */

/* > */

/* > \param[out] RCOND */

/* > \verbatim */

/* > RCOND is REAL */

/* > The estimate of the reciprocal condition number of the matrix */

/* > A after equilibration (if done). If RCOND is less than the */

/* > machine precision (in particular, if RCOND = 0), the matrix */

/* > is singular to working precision. This condition is */

/* > indicated by a return code of INFO > 0. */

/* > \endverbatim */

/* > */

/* > \param[out] FERR */

/* > \verbatim */

/* > FERR is REAL array, dimension (NRHS) */

/* > The estimated forward error bound for each solution vector */

/* > X(j) (the j-th column of the solution matrix X). */

/* > If XTRUE is the true solution corresponding to X(j), FERR(j) */

/* > is an estimated upper bound for the magnitude of the largest */

/* > element in (X(j) - XTRUE) divided by the magnitude of the */

/* > largest element in X(j). The estimate is as reliable as */

/* > the estimate for RCOND, and is almost always a slight */

/* > overestimate of the true error. */

/* > \endverbatim */

/* > */

/* > \param[out] BERR */

/* > \verbatim */

/* > BERR is REAL array, dimension (NRHS) */

/* > The componentwise relative backward error of each solution */

/* > vector X(j) (i.e., the smallest relative change in */

/* > any element of A or B that makes X(j) an exact solution). */

/* > \endverbatim */

/* > */

/* > \param[out] WORK */

/* > \verbatim */

/* > WORK is COMPLEX array, dimension (2*N) */

/* > \endverbatim */

/* > */

/* > \param[out] RWORK */

/* > \verbatim */

/* > RWORK is REAL array, dimension (N) */

/* > On exit, RWORK(1) contains the reciprocal pivot growth */

/* > factor norm(A)/norm(U). The "f2cmax absolute element" norm is */

/* > used. If RWORK(1) is much less than 1, then the stability */

/* > of the LU factorization of the (equilibrated) matrix A */

/* > could be poor. This also means that the solution X, condition */

/* > estimator RCOND, and forward error bound FERR could be */

/* > unreliable. If factorization fails with 0<INFO<=N, then */

/* > RWORK(1) contains the reciprocal pivot growth factor for the */

/* > leading INFO columns of A. */

/* > \endverbatim */

/* > */

/* > \param[out] INFO */

/* > \verbatim */

/* > INFO is INTEGER */

/* > = 0: successful exit */

/* > < 0: if INFO = -i, the i-th argument had an illegal value */

/* > > 0: if INFO = i, and i is */

/* > <= N: U(i,i) is exactly zero. The factorization */

/* > has been completed, but the factor U is exactly */

/* > singular, so the solution and error bounds */

/* > could not be computed. RCOND = 0 is returned. */

/* > = N+1: U is nonsingular, but RCOND is less than machine */

/* > precision, meaning that the matrix is singular */

/* > to working precision. Nevertheless, the */

/* > solution and error bounds are computed because */

/* > there are a number of situations where the */

/* > computed solution can be more accurate than the */

/* > value of RCOND would suggest. */

/* > \endverbatim */

/* Authors: */

/* ======== */

/* > \author Univ. of Tennessee */

/* > \author Univ. of California Berkeley */

/* > \author Univ. of Colorado Denver */

/* > \author NAG Ltd. */

/* > \date April 2012 */

/* > \ingroup complexGBsolve */

/* ===================================================================== */

/* Subroutine */ void cgbsvx_(char *fact, char *trans, integer *n, integer *kl,

*ferr, real *berr, complex *work, real *rwork, integer *info)

{

/* System generated locals */

integer ab_dim1, ab_offset, afb_dim1, afb_offset, b_dim1, b_offset,

x_dim1, x_offset, i__1, i__2, i__3, i__4, i__5;

real r__1, r__2;

complex q__1;

/* Local variables */

real amax;

char norm[1];

integer i__, j;

extern logical lsame_(char *, char *);

real rcmin, rcmax, anorm;

extern /* Subroutine */ void ccopy_(integer *, complex *, integer *,

complex *, integer *);

logical equil;

integer j1, j2;

extern real clangb_(char *, integer *, integer *, integer *, complex *,

integer *, real *);

extern /* Subroutine */ void claqgb_(integer *, integer *, integer *,

integer *, complex *, integer *, real *, real *, real *, real *,

real *, char *), cgbcon_(char *, integer *, integer *,

integer *, complex *, integer *, integer *, real *, real *,

complex *, real *, integer *);

real colcnd;

extern real clantb_(char *, char *, char *, integer *, integer *, complex

*, integer *, real *);

extern /* Subroutine */ void cgbequ_(integer *, integer *, integer *,

integer *, complex *, integer *, real *, real *, real *, real *,

real *, integer *);

extern real slamch_(char *);

extern /* Subroutine */ void cgbrfs_(char *, integer *, integer *, integer

*, integer *, complex *, integer *, complex *, integer *, integer

*, complex *, integer *, complex *, integer *, real *, real *,

complex *, real *, integer *), cgbtrf_(integer *, integer

*, integer *, integer *, complex *, integer *, integer *, integer

*);

logical nofact;

extern /* Subroutine */ void clacpy_(char *, integer *, integer *, complex

*, integer *, complex *, integer *);

extern int xerbla_(char *, integer *, ftnlen);

real bignum;

extern /* Subroutine */ void cgbtrs_(char *, integer *, integer *, integer

*, integer *, complex *, integer *, integer *, complex *, integer

*, integer *);

integer infequ;

logical colequ;

real rowcnd;

logical notran;

real smlnum;

logical rowequ;

real rpvgrw;

/* -- LAPACK driver routine (version 3.7.0) -- */

/* -- LAPACK is a software package provided by Univ. of Tennessee, -- */

/* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- */

/* April 2012 */

/* ===================================================================== */

/* Moved setting of INFO = N+1 so INFO does not subsequently get */

/* overwritten. Sven, 17 Mar 05. */

/* ===================================================================== */

/* Parameter adjustments */

ab_dim1 = *ldab;

ab_offset = 1 + ab_dim1 * 1;

ab -= ab_offset;

afb_dim1 = *ldafb;

afb_offset = 1 + afb_dim1 * 1;

afb -= afb_offset;

--ipiv;

--r__;

--c__;

b_dim1 = *ldb;

b_offset = 1 + b_dim1 * 1;

b -= b_offset;

x_dim1 = *ldx;

x_offset = 1 + x_dim1 * 1;

x -= x_offset;

--ferr;

--berr;

--work;

--rwork;

/* Function Body */

*info = 0;

nofact = lsame_(fact, "N");

equil = lsame_(fact, "E");

notran = lsame_(trans, "N");

if (nofact || equil) {

*(unsigned char *)equed = 'N';

rowequ = FALSE_;

colequ = FALSE_;

} else {

rowequ = lsame_(equed, "R") || lsame_(equed,

"B");

colequ = lsame_(equed, "C") || lsame_(equed,